Name 17.3 Geometry and Measurement—3.7.B MATHEMATICAL PROCESSES 3.1.A, 3.1.F Find Unknown Side Lengths ALGEBRA ? Essential Question How can you find the unknown length of a side in a polygon when you know its perimeter? Unlock Unlock the the Problem Problem Chen has 27 feet of fencing to put around his garden. He has already used the lengths of fencing shown. How much fencing does he have left for the last side? 7 ft 3 ft 4 ft 5 ft n Find the unknown side length. Write an equation for the perimeter. 5 + 3 + _ + _ + n = 27 Think: If I knew the length of n, I would add all the side lengths to find the perimeter. 5+3+ Add the lengths of the sides you know. 7 + 4 + n = 27 + n = 27 _ Think: Addition and subtraction are inverse operations. n = 27 − 19 Write a related equation. _ = 27 − 19 So, Chen has _ feet of fencing left. Math Idea Example Find unknown side lengths A symbol or letter can stand for an unknown side length. of a square. The square has a perimeter of 20 inches. What is the length of each side of the square? © Houghton Mifflin Harcourt Publishing Company Think: A square has four sides that are equal in length. s s You can multiply to find the perimeter. s s • Write a multiplication equation for the perimeter. 4× s = 20 • Use a multiplication fact you know to solve. 4 × _ = 20 So, the length of each side of the square is _ inches. Module 17 557 5 ft Example Find unknown side lengths of a rectangle. Hint: A rectangle has two pairs of opposite sides that are equal in length. Lauren has a rectangular blanket. The perimeter is 28 feet. The width of the blanket is 5 feet. What is the length of the blanket? l l • Add the lengths of the sides you know. _+_=_ • Subtract the lengths from the perimeter. 28 − _ = _ 5 ft • Divide the difference by 2. _÷2=_ So, the length of the blanket is _ feet. Share Share and and Show Show Find the unknown side lengths. 1. Perimeter = 25 centimeters 9 cm 9 + _ + _ + n = 25 6 cm n + n = 25 3 cm n = _ centimeters _=_−_ 2. Perimeter = 34 meters 3. Perimeter = 12 feet j 7m r 7m r r r j j = _ meters 558 r = _ feet Math Talk Mathematical Processes Explain how you can use division to find the length of a side of a square. © Houghton Mifflin Harcourt Publishing Company _ Name Unlock Unlock the the Problem Problem 4. Multi-Step Use Diagrams Latesha wants to make a border with ribbon around a figure she made and sketched at the right. She will use 44 centimeters of ribbon for the border. What is the unknown side length? A 3 centimeters C 9 centimeters B 13 centimeters D 6 centimeters 3 cm 8 cm 13 cm 6 cm 5 cm h a. What do you need to find? _________ b. How will you use what you know about perimeter to help you solve the problem? __________ c. Write an equation to solve the problem. d. Complete the sentences. The perimeter is _ centimeters. The sum of the sides I know is _ centimeters. A related subtraction equation is _ = _ − _. So, the length of side h is _ centimeters. © Houghton Mifflin Harcourt Publishing Company e. 5. Fill in the bubble for the correct answer choice above. Multi-Step A rectangle has a perimeter of 34 inches. The left side is 6 inches long. What is the length of the top side? Module 17 • Lesson 3 559 Mathematical Processes M Model ¥ Reason ¥ Communicate M Daily Daily Assessment Assessment Task Task Fill in the bubble completely to show your answer. 6. 7. 8. A wildlife sanctuary puts a fence around a section of their land. The fence is 19 kilometers long. What is the length of the unknown side? A 5 kilometers C 33 kilometers B 7 kilometers D 14 kilometers 2 km 4 km 4 km n 4 km Ciara buys a piece of ribbon to sew around the edges of a square blanket. She uses 36 inches of ribbon. How long is each side of the blanket? A 18 inches C 4 inches B 9 inches D 32 inches Multi-Step Kenny puts a fence around his 5-sided garden. He starts with 35 feet of fencing. After he is done, he has 5 feet of fencing left over. How long is each side of his garden? A 7 feet C 6 feet B 5 feet D 3 feet g g g g g TEXAS Test Prep 560 Eleni wants to put a fence around her square garden. The garden has a perimeter of 28 meters. How long will each side of the fence be? A 8 meters B 7 meters C 14 meters D 6 meters a a a a © Houghton Mifflin Harcourt Publishing Company 9. Geometry and Measurement—3.7.B MATHEMATICAL PROCESSES 3.1.A, 3.1.F H o mewo rk and Practice 17.3 Name Find Unknown Side Lengths ALGEBRA Find the unknown side lengths. 1. Perimeter = 28 centimeters 2. Perimeter = 40 feet 11 feet m 6 cm 6 cm g g 11 feet m m = _ centimeters g = _ feet Problem Problem Solving Solving x Use the diagram for 3–4. © Houghton Mifflin Harcourt Publishing Company 3. Mitch needs to replace the fence in his backyard. The diagram shows the lengths of the borders of the fence. The length of the fence is 62 meters. What is the unknown side length? Explain how you will solve the problem. Then write an equation to solve the problem. 5m 12 m 7m 5m 14 m 4. What if Mitch changes the shape of his fence to a rectangle? How much fencing will Mitch need? Explain. Module 17 • Lesson 3 561 TEXAS Test Prep Lesson Lesson Check Check Fill in the bubble completely to show your answer. Nagi has a mirror in the shape of a hexagon. He puts a frame around it that has a perimeter of 42 inches. 6. How long is each side? 7. 8. 562 A 7 inches C 8 inches B 6 inches D 9 inches Zena has a square picture frame with a perimeter of 28 inches. Which equation can she use to find the length of each side? A 4 × s = 28 B 4 + s = 28 C 28 × 4 = s D 28 + 4 = s A farmer is putting a new fence around a section of his ranch. The fence is 35 kilometers long. What is the length of the unknown side? A 6 kilometers B 29 kilometers C 7 kilometers D 35 kilometers 5 km 8 km x 7 km 9 km Multi-Step Glenda puts a border of wallpaper around her bedroom wall. The room is a rectangle with side lengths of 3 meters and 4 meters. If she has 20 meters of wallpaper, how much wallpaper is left over? 9. Multi-Step Jorge sews a trim around the edge of a tablecloth with 8 sides. He has 32 feet of trim. If each side of the tablecloth is 2 feet long, how much trim will Jorge have left? A 13 meters C 27 meters A 10 feet C 42 feet B 6 meters D 14 meters B 8 feet D 16 feet © Houghton Mifflin Harcourt Publishing Company 5. Name Module 17 Assessment Vocabulary Vocabulary Vocabulary Choose the best term from the box. 1. area The distance around a figure is the __. perimeter (p. 545) Concepts Concepts and and Skills Skills Find the perimeter of the figure. Each unit is 1 centimeter. 2. 3. _ centimeters _ centimeters Find the unknown side lengths. 4. q TEKS 3.7.B Perimeter = 33 centimeters 5. Perimeter = 32 feet 10 cm 12 ft 4 cm 6 cm k g k 12 ft 10 cm 6. q TEKS 3.7.B g = _ centimeters k = _ centimeters Use a centimeter ruler to find the perimeter. q TEKS 3.7.B © Houghton Mifflin Harcourt Publishing Company cm cm cm cm cm cm _ centimeters Module 17 563 Fill in the bubble for the correct answer choice. 8. 9. 10. 11. 564 m Jacob built a toolbox with a perimeter of 70 inches. What is the length of side m? q TEKS 3.7.B A 50 inches B 20 inches C 25 inches D 10 inches 10 in. 10 in. m Adrienne is decorating a square picture frame. She glued 32 inches of ribbon around the edge of the frame. What is the length of each side of the picture frame? q TEKS 3.7.B A 4 inches C 28 inches B 8 inches D 16 inches a a a a What is the perimeter of the figure? Each unit is 1 centimeter. q TEKS 3.7.B A 20 centimeters C 23 centimeters B 18 centimeters D 9 centimeters Jeff is making a poster for a car wash for the Campout Club. What is the perimeter of the poster? q TEKS 3.7.B A 8 feet C 6 feet B 3 feet D 4 feet 3 ft 1 ft A rectangle has side lengths of 8 inches and 10 inches. What is the perimeter of the rectangle? q TEKS 3.7.B A 28 inches C 32 inches B 18 inches D 36 inches 1 ft 3 ft © Houghton Mifflin Harcourt Publishing Company 7. TEXAS Test Prep

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